T-rough symmetric Heyting algebras with tense operators

Abstract

T-rough Heyting algebras were introduced by Eric SanJuan in 2008 as an algebraic formalism for reasoning on finite increasing sequences over Boolean algebras in general and on generalizations of rough set concepts in particular. In this paper, we introduce the variety of algebras, which we call T-rough symmetric Heyting algebras. These algebras constitute an extension of T-rough Heyting algebras and a generalization of symmetric Heyting algebras of order n. Our main interest is the representation theory of tense operators on T-rough symmetric Heyting algebras. In order to do this, a discrete-style duality for these algebras is developed.